login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173441 Number of divisors d of n such that sigma(d) divides n. 8
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
From Robert Israel, Oct 11 2017: (Start)
a(n) >= 1 since d=1 is always included.
a(n) = 1 if n is in A000961.
a(n) > 1 if n is in A097603. The first n not in A097603 such that a(n) > 1 is 117. (End)
LINKS
FORMULA
a(n) = A000005(n) - A173442(n). - A-number inserted by R. J. Mathar, Mar 06 2010
EXAMPLE
For n = 12, a(12) = 4; divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) divides n for 4 divisors d: 1, 2, 3, 6.
MAPLE
f:= proc(n) nops(select(t -> n mod numtheory:-sigma(t) = 0, numtheory:-divisors(n))) end proc:
map(f, [$1..100]); # Robert Israel, Oct 11 2017
MATHEMATICA
a[n_] := Select[Divisors[n], Divisible[n, DivisorSigma[1, #]]&] // Length;
Array[a, 100] (* Jean-François Alcover, Jun 05 2020 *)
PROG
(PARI) a(n) = sumdiv(n, d, !(n % sigma(d))); \\ Michel Marcus, Oct 11 2017
CROSSREFS
Sequence in context: A010248 A325403 A132068 * A326851 A129192 A062540
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 18 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 29 23:21 EST 2024. Contains 370428 sequences. (Running on oeis4.)